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Expresión d*(-c*(-a)*(-b)+c*(-(-a)*(-b)))

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    Solución

    Ha introducido [src]
    d∧((c∧(¬b)∧(¬(¬a)))∨((¬a)∧(¬b)∧(¬c)))
    d((c¬b¬(¬a))(¬a¬b¬c))d \wedge \left(\left(c \wedge \neg b \wedge \neg \left(\neg a\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right)\right)
    Solución detallada
    ¬(¬a)=a\neg \left(\neg a\right) = a
    c¬b¬(¬a)=ac¬bc \wedge \neg b \wedge \neg \left(\neg a\right) = a \wedge c \wedge \neg b
    (c¬b¬(¬a))(¬a¬b¬c)=¬b(a¬c)(c¬a)\left(c \wedge \neg b \wedge \neg \left(\neg a\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right) = \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)
    d((c¬b¬(¬a))(¬a¬b¬c))=d¬b(a¬c)(c¬a)d \wedge \left(\left(c \wedge \neg b \wedge \neg \left(\neg a\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right)\right) = d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)
    Simplificación [src]
    d¬b(a¬c)(c¬a)d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)
    d∧(¬b)∧(a∨(¬c))∧(c∨(¬a))
    Tabla de verdad
    +---+---+---+---+--------+
    | a | b | c | d | result |
    +===+===+===+===+========+
    | 0 | 0 | 0 | 0 | 0      |
    +---+---+---+---+--------+
    | 0 | 0 | 0 | 1 | 1      |
    +---+---+---+---+--------+
    | 0 | 0 | 1 | 0 | 0      |
    +---+---+---+---+--------+
    | 0 | 0 | 1 | 1 | 0      |
    +---+---+---+---+--------+
    | 0 | 1 | 0 | 0 | 0      |
    +---+---+---+---+--------+
    | 0 | 1 | 0 | 1 | 0      |
    +---+---+---+---+--------+
    | 0 | 1 | 1 | 0 | 0      |
    +---+---+---+---+--------+
    | 0 | 1 | 1 | 1 | 0      |
    +---+---+---+---+--------+
    | 1 | 0 | 0 | 0 | 0      |
    +---+---+---+---+--------+
    | 1 | 0 | 0 | 1 | 0      |
    +---+---+---+---+--------+
    | 1 | 0 | 1 | 0 | 0      |
    +---+---+---+---+--------+
    | 1 | 0 | 1 | 1 | 1      |
    +---+---+---+---+--------+
    | 1 | 1 | 0 | 0 | 0      |
    +---+---+---+---+--------+
    | 1 | 1 | 0 | 1 | 0      |
    +---+---+---+---+--------+
    | 1 | 1 | 1 | 0 | 0      |
    +---+---+---+---+--------+
    | 1 | 1 | 1 | 1 | 0      |
    +---+---+---+---+--------+
    FNDP [src]
    (acd¬b)(d¬a¬b¬c)\left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right)
    (a∧c∧d∧(¬b))∨(d∧(¬a)∧(¬b)∧(¬c))
    FNC [src]
    Ya está reducido a FNC
    d¬b(a¬c)(c¬a)d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)
    d∧(¬b)∧(a∨(¬c))∧(c∨(¬a))
    FNCD [src]
    d¬b(a¬c)(c¬a)d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)
    d∧(¬b)∧(a∨(¬c))∧(c∨(¬a))
    FND [src]
    (acd¬b)(ad¬a¬b)(cd¬b¬c)(d¬a¬b¬c)\left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(a \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge d \wedge \neg b \wedge \neg c\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right)
    (a∧c∧d∧(¬b))∨(a∧d∧(¬a)∧(¬b))∨(c∧d∧(¬b)∧(¬c))∨(d∧(¬a)∧(¬b)∧(¬c))